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Results tagged with set-theory
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user 144779
forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
29
votes
3
answers
3k
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Are there substantive differences between the different approaches to "size issues" in categ...
In category theory, there are different ways to approach the "size issues" that crop up when we try to formalise the subject in axiomatic set theory. As far as I can tell, there are two main approache …
- 961
7
votes
Implicit uses of Countable or Dependent Choice
The axiom of dependent choice is sometimes implicitly used in the context of chain conditions in algebra.
If $(X,\le)$ is a partially ordered set, then we say that it is well-founded if every nonempty …
15
votes
5
answers
2k
views
In what sense does the sentence $\operatorname{con}(\mathsf{PA})$ "say" that $\mathsf{PA}$ i...
It seems common amongst logicians to think of "truth" as being relative to a particular structure. Consider, for instance, the first-order theory of groups. The sentence $\forall x\forall y(x\cdot y=y …
- 961